I'd ask your friend why she thinks her dislike of this other person would create any obligation in you to behave in any specific fashion. This other person cancelled a date with your friend, sure--what's that got to do with you? Does she think you need her permission to date people? Why does she seem to have a problem with you deciding how you'll interact with others on your own? Why does she think she has some control over you?

I don't have an answer for you. I was trying to work things out and talk with her to see if I was missing something in why she was feeling the way she is. All I could get her to tell me though was that she needed space. So space is what I will give her. She knows where I am if she comes to the place where she wants to have a friendship with me.